In [1]} (see pages 37–39) a construction
of a universal fiberwise principal \(G\) -bundle is given, where \(G\)  is a
group object in \({K}/B\) . This construction is based on the Milnor
construction of a universal bundle, using infinite joins. This
model of the universal bundle is very useful as it makes almost no
assumptions on \(G\) , however it is also useful to impose a mild restriction
on \(G\)  and build a slightly more economical model with some convenient properties.
